4. Consider a farmer who can either plant or market/consume his crop. Whatever amount he plants becomes a crop twice the size the following year. For example, if he plants seed from 2 ears of corn, he gets 4 ears of corn at harvest. Assume he starts off with 50 bushels of corn.

a. If he decides every year to market/consume half his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?

b. If he decides every year to market/consume 2/5 of his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?

c. Compare the consumption of the farmer in each of the first five years under plans a. and b.

d. Why might the results of plan b. not be realistic?

5. Imagine the following goal of Lenin/Stalin at the beginning of the Soviet regime in Russia: to overtake (i.e. equal) and surpass the worldâs industrialized economies in terms of GDP per capita. To achieve this goal, the main instrument of control is the fraction of national production that is devoted to building the nationâs productive capacity: new machines, factories, transportation equipment, and roads. That is, the main instrument to achieve this goal is what fraction of GDP to devote to investment. The rest of national production is used for consumption, i.e. to produce consumer items like clothing and food. The country begins with relatively little capital, being mostly rural and non-industrialized. Assume each of the following: ï· GDP per capita starts in USSR at $300/year. ï· The worldâs industrialized economies start with GDP per capita of $5000/year. ï· Population growth rates are 2% everywhere in the world. ï· All capital depreciates at 8% per year.

a. At what average annual rate will income per capita in the USSR have to grow in order to overtake (i.e. to equal) the industrialized nationsâ income per capita in exactly 30 years? Assume the industrialized nationsâ income per capita is growing at 2% per year.

b. If the USSR sustains the growth rate of part a., how long after it has overtaken the industrialized nationsâ GDP per capita will it take for it to attain double the industrialized nationsâ GDP per capita? Again, assume the industrialized nationsâ GDP per capita is growing at 2% per year. For parts c.-e., assume the basic growth framework of Harrod-Domar, and that 1 rubleâs worth of capital always produces 0.5 rubleâs worth of output (i.e. A=0.5). Also, assume inputs are used more efficiently in the industrialized countries, so that A=0.6 there.

c. What fraction of national output must the USSR devote to building new capital goods in order to attain the growth rate of part a.? What fraction would be left for consumer items? [Hint: another word for the fraction of output devoted to building new capital goods is the investment rate, i.e. the ratio It/Yt. And, remember that savings equals investment, so the investment rate equals the savings rate.]

d. At what rate are the industrialized countries saving if they are growing at 2% per year? e. What would you calculate the ratio of consumption per capita in the USSR to consumption per capita in the industrialized countries when the USSR overtakes the industrialized countries (i.e. when GDP per capita is equal)? Assume the savings rates of parts c. & d. What would the ratio be when the USSR reaches double the industrialized nationsâ GDP per capita?

4. Consider a farmer who can either plant or market/consume his crop. Whatever amount he plants becomes a crop twice the size the following year. For example, if he plants seed from 2 ears of corn, he gets 4 ears of corn at harvest. Assume he starts off with 50 bushels of corn.

a. If he decides every year to market/consume half his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?

b. If he decides every year to market/consume 2/5 of his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?

c. Compare the consumption of the farmer in each of the first five years under plans a. and b.

d. Why might the results of plan b. not be realistic?

5. Imagine the following goal of Lenin/Stalin at the beginning of the Soviet regime in Russia: to overtake (i.e. equal) and surpass the worldâs industrialized economies in terms of GDP per capita. To achieve this goal, the main instrument of control is the fraction of national production that is devoted to building the nationâs productive capacity: new machines, factories, transportation equipment, and roads. That is, the main instrument to achieve this goal is what fraction of GDP to devote to investment. The rest of national production is used for consumption, i.e. to produce consumer items like clothing and food. The country begins with relatively little capital, being mostly rural and non-industrialized. Assume each of the following: ï· GDP per capita starts in USSR at $300/year. ï· The worldâs industrialized economies start with GDP per capita of $5000/year. ï· Population growth rates are 2% everywhere in the world. ï· All capital depreciates at 8% per year.

a. At what average annual rate will income per capita in the USSR have to grow in order to overtake (i.e. to equal) the industrialized nationsâ income per capita in exactly 30 years? Assume the industrialized nationsâ income per capita is growing at 2% per year.

b. If the USSR sustains the growth rate of part a., how long after it has overtaken the industrialized nationsâ GDP per capita will it take for it to attain double the industrialized nationsâ GDP per capita? Again, assume the industrialized nationsâ GDP per capita is growing at 2% per year. For parts c.-e., assume the basic growth framework of Harrod-Domar, and that 1 rubleâs worth of capital always produces 0.5 rubleâs worth of output (i.e. A=0.5). Also, assume inputs are used more efficiently in the industrialized countries, so that A=0.6 there.

c. What fraction of national output must the USSR devote to building new capital goods in order to attain the growth rate of part a.? What fraction would be left for consumer items? [Hint: another word for the fraction of output devoted to building new capital goods is the investment rate, i.e. the ratio It/Yt. And, remember that savings equals investment, so the investment rate equals the savings rate.]

d. At what rate are the industrialized countries saving if they are growing at 2% per year? e. What would you calculate the ratio of consumption per capita in the USSR to consumption per capita in the industrialized countries when the USSR overtakes the industrialized countries (i.e. when GDP per capita is equal)? Assume the savings rates of parts c. & d. What would the ratio be when the USSR reaches double the industrialized nationsâ GDP per capita?